Preprint

Inserted: 10 oct 2023
Last Updated: 23 nov 2023

Year: 2023

Abstract:

We prove a new class of $L^2$-weighted elliptic estimates on smooth two-manifolds for positive weights $\omega$ that formally satisfy $\omega^2\Delta\ln(\omega) = -\kappa(x)\omega^2$. The proof is short and relies on a lemma about symmetric two dimensional matrices.